The only reason that Plex has survived every service purge on my system is because Jellyfin doesn’t have a PS4 app. Every other device that accesses my media is going through Jellyfin. I have my PS4 connected to Jellyfin via DLNA, but asking my wife to give up the polished (turd) Plex app for the file-picker front end in the media player app isn’t a viable option for me.
Does a Firestick require WAN access? I know my PS4 calls out of the network pretty regularly, but I’m a little hesitant to add more data harvesting into my network. I haven’t ruled it out, though.
I can’t recall offhand. What I will say, though, is that your PS4 is not designed to be a streaming device. It can utilize streaming apps, but that is not its purpose or focus. The apps available on its platform will always be a step behind those for dedicated streaming devices such as Firestick, Roku, Chromecast, AppleTV, or specific streaming apps on a smart TV.
If you are concerned about data harvesting, you should migrate away from Plex and onto something open source like Jellyfin overall. Once Plex closed their code and pushed towards monetization, they began harvesting data just like any other streaming service. That said, there is no Jellyfin app on PS4, but it is fully accessible through the PS4. Again, however, your PS4 is not really meant to be your all-encompassing streaming platform. A Roku or Firestick is very cheap, it is designed to only stream apps, both of Jellyfin, and Plex if you need to continue on that path, and will provide a far better viewing experience than a PS4.